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Properties

Label 310206.q
Number of curves $2$
Conductor $310206$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 310206.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310206.q1 310206q2 \([1, 0, 0, -237433631, -4362373486803]\) \(-1480302302050395483730662419569/7364359653002993324767146804\) \(-7364359653002993324767146804\) \([]\) \(190236032\) \(4.0316\)  
310206.q2 310206q1 \([1, 0, 0, -18645971, 31710685857]\) \(-716933257039953084158724529/19555843924966303678464\) \(-19555843924966303678464\) \([7]\) \(27176576\) \(3.0587\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 310206.q have rank \(0\).

Complex multiplication

The elliptic curves in class 310206.q do not have complex multiplication.

Modular form 310206.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} + q^{13} + q^{14} - q^{15} + q^{16} - 3 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.